Trouble replicating the animation where the colour only spreads onto a specific area
Even though you have part of the process completed, I will give an overview of the steps.
You could transform all images in the node editor, but since Blenders transformation nodes are inefficient to handle, I will suggest the 3D space.

Load your image into the compositor. Set the project size to match it's dimensions.
I will use the images as planes addon to quickly get my ink movie clip into the 3D view. Import it with the options Auto Refresh and Shadeless.
Then I added an orthographic camera. The movie clip should play, if you selected auto-refresh.
Set the image as a background image in the 3D view. Transform the movie clip plane in camera view.
Set the World Background to black. The render will be used as a mask based in the luminance.
Mask the image in the Movie Clip Editor.

Load your Renderlayer and Mask into the compositor and multiply them with a ColorMix node.
To color the masked portion red, use a ColorMix node. Connect the multiplied masks with the Fac input.

Rendering it results in the desired effect.

Further notes.

If you change your scene size (using the percentage slider), you will need to add a scale node to the Input Image.
If the ink movie clip mask is not white, the effect will not be 100% opaque. You a RGB Curves node or a colorramp to shift its whitepoint.
You can use the mask with many other nodes other than a MixRGB node.